Rachel98
I don't really get this.
Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2



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mjr632
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Do you mean a rigorous formal proof?

Rachel98
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I don't really know. This is what the question was and I don't get it.

mjr632
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Do you understand how to use logarithms?

Rachel98
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No

mjr632
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Ah, you will want to understand natural logarithms for this question, I can explain it.

mjr632
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\[y = \log_b x\]
\[x = b^y\]

mjr632
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If we take the natural logarithm of \[512^{\frac{2}{3}}\]
\[\frac{2}{3}\ln(512)\]

mjr632
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We can pull the exponent out

Rachel98
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So, is that a cube root? That we ended up with?

precal
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dw:1360950294527:dw

precal
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dw:1360950347726:dw

precal
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dw:1360950360574:dw

precal
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dw:1360950390774:dw

precal
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dw:1360950432326:dw

precal
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yes they are both equivalent

Rachel98
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Thanks, so much. That makes sense now.

precal
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yw

precal
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no need to use logs here

ghass1978
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just using exponents :512=2^9
so 512^(2/3)=2^6
and 16^(3/2)=2^6 so both are equal

Rachel98
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Thanks

precal
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yw